A sealed bid first price auction requires bidders to submit bids in a sealed envelope, or in an electronic equivalent of a sealed envelope, such that all bids are kept secret from rival bidders and each bidder only gets one bid. The highest bidder (or the lowest bidder in the instance of a procurement auction) is deemed the winner. A bidder participating in a sealed bid first price auction must make a number of decisions when determining a bid. In order to assist a bidder in determining their optimal bid, various tools have been developed for analyzing a particular market environment.
In game theoretic approach, auctions are modeled as games of incomplete information played by Bayesian players. Basic elements of models of auctions-as-games include a set of bidders, a set of types for each bidder representing the bidder's private information, and a set of conditional probabilities representing the bidder's beliefs about rival bidders' types conditional on his/her own type.
In game theoretic approach, the joint distribution of bidders' valuations is taken as a key structural element of the auction environment. All the theoretical results—bidding behavior, comparison of alternative auction mechanisms, etc.—are expressed in terms of the joint value distribution. However, in practice the key structural elements of the auction environment are unobservable. As such, the usefulness of current bid determination tools is limited. To overcome this shortcoming, it has been proposed to express the results of the bid determination in terms of the joint bid distribution in working with the historical bidding data.
This approach, however, maintains Nash equilibrium behavior on the part of the bidders as an assumption. By the very same assumption, all the observed bids in the sample of auctions analyzed by the econometrician are treated as equilibrium bids. In particular, the informational assumptions of the game model are taken as starting point. That is, the structural elements of the game are unknown only to the econometrician analyzing the data, but not to the bidders or the seller. As far as the bidders are concerned, they are assumed to know the joint distribution of all valuations. Furthermore, being Bayesians, the bidders correctly guess the rival bidders' bidding behavior.
Provided such strong informational assumptions are maintained, other considerations necessitate even stronger assumptions—such as symmetry, risk neutrality—to render equilibrium approach applicable in situations with practically realistic sample sizes and data structures.
Currently, a typical bidder's model of the bidding environment features the details typically assumed in game theoretic equilibrium analysis of auctions. In particular, a bidder makes a number of assumptions, including but not limited to how rival bidders' valuations are determined, what bidding strategies rival bidders adopt, what the risk attitudes of rival bidders are, and how many rival bidders may participate in the auction.
Current tools for determining an optimal bid in a sealed bid first price auction analyze bid data from historical auctions. The historical bid data is used to determine the probability of winning the auction given alternate bid amounts. However, in order to determine the bid amounts, a number of assumptions are relied on. In particular, it is commonly assumed that the bidders' valuations, and hence, their bids, are independent of each other. In essence, it is assumed that a bidder will not change their bid if the bidder becomes aware of the bid of another bidder or bidders. Making conclusions relying on the independence assumption provides less reliable bid information, and may lead to an incorrect bid strategy.
Current methods for determining an optimal bid in a first bid sealed price auction have substantial drawbacks. One class of methods provide solutions that are theoretical, and are not suited for practical use. Furthermore, other methods require the use of broad assumptions to determine the bidders' valuations, thus limiting the applicability and reliability of the results.